Camera following a rig question
IF what you want is a rigid, mechanical way for the camera to follow the guy, you should put an empty where you want the camera to look, parent that empty to the guy (so that it follows him when he moves), and then add a "Track to..." constraint, with that empty as a target.

This will produce what you're asking for, but as Abedd pointed out, I don't think that's what you want.

This problem has been solved before, in two different ways. One way is to just make the camera do what you want it to do. It might mean you have a keyframe on every frame (probably not), but it'll look at what you want, when you want it to look there.

The REAL solution is a genuine camera rig. You build an armature for your camera that makes it move more like a real camera does. you build different rigs for handhelds, locked shots, crane shots, and Steadicam shots. There are also existing rigs that you could get from elsewhere. I'll bet there's one on BlendSwap, but I haven't looked.

The best solution for you, right now, is probably a really simple rig. Don't spend too much time trying to learn a new skill and new rig, just make an empty that's easy to move around and make your camera look at it. Then you can animate it and the camera at the same time. Don't parent the empty to anything, just use it to control where the camera is looking.